On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions

Rezapour S., Kumar S., Iqbal M., Hussain A., Etemad S.

Mathematics and Computers in Simulation, vol.194, pp.365-382, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 194
  • Publication Date: 2022
  • Doi Number: 10.1016/j.matcom.2021.11.018
  • Journal Name: Mathematics and Computers in Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Page Numbers: pp.365-382
  • Keywords: Fixed point, Fractional operators, L1-caratheodory, Multi-functions, Multi-term sequential boundary problem
  • Uşak University Affiliated: No

Abstract

In this research, we investigate some conditions on the existence of solutions for two abstract multi-term sequential boundary value problems defined with the help of the Caputo derivatives. To do this, we consider some hypotheses on the existing single-valued and multi-valued functions defined in the given fractional differential equation and inclusion. In fact, according to the conditions of two versions of the Krasnoselskii's fixed point theorems, we prove our required criteria which confirm the existence of solutions for the suggested boundary value problems. Finally, we consider some examples to show the consistency of our results numerically.